To solve \( 1 \frac{1}{5} \div \frac{3}{4} \), we follow these steps:

1. Convert the mixed number \( 1 \frac{1}{5} \) into an improper fraction:
   \[
   1 \frac{1}{5} = \frac{6}{5}
   \]

2. Now, divide \( \frac{6}{5} \) by \( \frac{3}{4} \), which is the same as multiplying by the reciprocal of \( \frac{3}{4} \):
   \[
   \frac{6}{5} \div \frac{3}{4} = \frac{6}{5} \times \frac{4}{3}
   \]

3. Multiply the numerators and the denominators:
   \[
   \frac{6 \times 4}{5 \times 3} = \frac{24}{15}
   \]

4. Simplify \( \frac{24}{15} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
   \[
   \frac{24}{15} = \frac{8}{5}
   \]

So, the result is \( \frac{8}{5} \), which can also be written as \( 1 \frac{3}{5} \).

Would you like more details on any of these steps?

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Here are some related questions to think about:

1. How do you multiply fractions?
2. What is the process to convert improper fractions into mixed numbers?
3. How do you simplify fractions?
4. How do you divide fractions without converting them into decimals?
5. Why is dividing by a fraction equivalent to multiplying by its reciprocal?

**Tip**: Always simplify fractions at the end to get the most reduced form.

Learn how to solve the fraction division problem 1 1/5 ÷ 3/4 with a step-by-step guide. This detailed solution covers converting mixed numbers to improper fractions, multiplying by the reciprocal, and simplifying the result. Suitable for students in Grades 6-8.

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